Start listing terms (by Pigeonhole principle it must repeat),
a_1=5
a_2=7
a_3=6
a_4=14
a_5=10
a_6=12
a_7=11
a_8=4
a_9=0
a_10=2
a_11=1
a_12=9
a_13=5
Aha! It repeats.
Thus, find the remaind what 250 leaves upon divison by 12 (because it repeats after 12).
Which is 10.
Thus, it is the 10-th term in this sequence.